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 A127420 Triangle, read by rows, where row n+1 is generated from row n by first inserting zeros at positions {(m+2)*(m+3)/2, m>=0} in row n and then taking the partial sums in reverse order, for n>=2, starting with 1's in the initial two rows. 3
 1, 1, 1, 2, 1, 1, 4, 2, 2, 1, 9, 5, 5, 3, 1, 1, 24, 15, 15, 10, 5, 5, 2, 1, 77, 53, 53, 38, 23, 23, 13, 8, 3, 3, 1, 295, 218, 218, 165, 112, 112, 74, 51, 28, 28, 15, 7, 4, 1, 1, 1329, 1034, 1034, 816, 598, 598, 433, 321, 209, 209, 135, 84, 56, 28, 28, 13, 6, 2, 1, 6934, 5605 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Column 0 forms A091352, which also equals column 1 of table A125781, where table A125781 is generated by a complementary recurrence of this triangle. The number of terms in row n is A127419(n). LINKS EXAMPLE To generate row 6, start with row 5: 24, 15, 15, 10, 5, 5, 2, 1; insert zeros at positions [1,4,8,13,..., (m+2)*(m+3)/2 - 2,...]: 24, 0, 15, 15, 0, 10, 5, 5, 0, 2, 1; then row 6 equals the partial sums of row 5 taken in reverse order: 24, _0, 15, 15, _0, 10, _5, 5, 0, 2, 1; 77, 53, 53, 38, 23, 23, 13, 8, 3, 3, 1. Triangle begins: 1; 1, 1; 2, 1, 1; 4, 2, 2, 1; 9, 5, 5, 3, 1, 1; 24, 15, 15, 10, 5, 5, 2, 1; 77, 53, 53, 38, 23, 23, 13, 8, 3, 3, 1; 295, 218, 218, 165, 112, 112, 74, 51, 28, 28, 15, 7, 4, 1, 1; 1329, 1034, 1034, 816, 598, 598, 433, 321, 209, 209, 135, 84, 56, 28, 28, 13, 6, 2, 1; Column 0 of this triangle equals column 1 of triangle A091351, where triangle A091351 begins: 1; 1, 1; 1, 2, 1; 1, 4, 3, 1; 1, 9, 9, 4, 1; 1, 24, 30, 16, 5, 1; 1, 77, 115, 70, 25, 6, 1; 1, 295, 510, 344, 135, 36, 7, 1; ... and column k of A091351 = row sums of matrix power A091351^k for k>=0. CROSSREFS Cf. A091352, A091351, A125781, A127419. Sequence in context: A176452 A244581 A064191 * A129033 A054090 A239456 Adjacent sequences:  A127417 A127418 A127419 * A127421 A127422 A127423 KEYWORD nonn,tabf AUTHOR Paul D. Hanna, Jan 14 2007 STATUS approved

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Last modified October 15 14:07 EDT 2018. Contains 316236 sequences. (Running on oeis4.)