diff --git a/lifetimes/utils.py b/lifetimes/utils.py
index 332b6813..43525ac5 100644
--- a/lifetimes/utils.py
+++ b/lifetimes/utils.py
@@ -278,18 +278,19 @@ def calculate_alive_path(model, transactions, datetime_col, t, freq='D'):
     purchase_history = (customer_history.resample(freq).sum().replace(np.nan, 0)
                         ['transactions'].values)
 
-    extra_columns = t - len(purchase_history)
+    extra_columns = t + 1 - len(purchase_history)
     customer_history = pd.DataFrame(np.append(purchase_history, [0] * extra_columns), columns=['transactions'])
     # add T column
-    customer_history['T'] = np.arange(start=1,stop=customer_history.shape[0]+1)
+    customer_history['T'] = np.arange(customer_history.shape[0])
     # add cumulative transactions column
     customer_history['transactions'] = customer_history['transactions'].apply(lambda t: int(t>0))
     customer_history['frequency'] = customer_history['transactions'].cumsum() - 1  # first purchase is ignored
     # Add t_x column
-    customer_history['recency'] = customer_history.apply(lambda row: row['T']-1 if row['transactions'] != 0 else np.nan, axis=1)
+    customer_history['recency'] = customer_history.apply(lambda row: row['T'] if row['transactions'] != 0 else np.nan, axis=1)
     customer_history['recency'] = customer_history['recency'].fillna(method='ffill').fillna(0)
-    return customer_history.apply(lambda row: model.conditional_probability_alive(row['frequency'], row['recency'], row['T']), axis=1)
-
+    return customer_history.apply(
+        lambda row: model.conditional_probability_alive(row['frequency'], row['recency'], row['T']),
+        axis=1)
 
 def _fit(minimizing_function, minimizing_function_args, iterative_fitting,
          initial_params, params_size, disp, tol=1e-8, fit_method='Nelder-Mead',