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 A128590 Triangle read by rows, matrix product A128179 * A000012. 0
 1, 2, 2, 4, 3, 3, 6, 6, 4, 4, 9, 8, 8, 5, 5, 12, 12, 10, 6, 6, 16, 15, 15, 12, 12, 7, 7, 20, 20, 18, 18, 14, 14, 8, 8, 25, 24, 24, 21, 21, 16, 16, 9, 9, 30, 30, 28, 28, 24, 24, 18, 18, 10, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums = the tetrahedral numbers, A000292, starting (1, 4, 10, 20, 35, 56, 84, ...). LINKS FORMULA A128179 * A000012 as infinite lower triangular matrices. Regarded as an array by antidiagonals A(i, j) = degree in q of q-Fibonacci number F(i+2, j-1) where F(1, k) = F(2, k) = 1, F(n, k) = F(n-1, k) + q^(n+k-2) * F(n-2, k). - Michael Somos, Jun 08 2011 EXAMPLE First few rows of the triangle are: 1; 2, 2; 4, 3, 3; 6, 6, 4, 4; 9, 8, 8, 5, 5; 12, 12, 10, 6, 6; 16, 15, 15, 12, 12, 7, 7; ... First few rows of the array are: 1,  2,  3,  4,  5,  6,  7,  8, ... 2,  3,  4,  5,  6,  7,  8,  9, ... 4,  6,  8, 10, 12, 14, 16, 18, ... 6,  8, 10, 12, 14, 16, 18, 20, ... 9, 12, 15, 18, 21, 24, 27, 30, ... ... A(3, 4) = 10 because F(5, 3) = 1 + q^4 + q^5 + q^6 + q^10. A(4, 4) = 12 because F(6, 3) = 1 + q^4 + q^5 + q^6 + q^7 + q^10 + q^11 + q^12. PROG (PARI) {T(n, k) = (n - k + 2)\2 * ((n + k + 1)\2)} /* Michael Somos, Jun 08 2011 */ CROSSREFS Cf. A128179, A000012, A000292. Sequence in context: A147594 A212652 A205678 * A143228 A143211 A209755 Adjacent sequences:  A128587 A128588 A128589 * A128591 A128592 A128593 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Mar 11 2007 STATUS approved

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