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 A129503 Pascal's Fredholm-Rueppel triangle. 2
 1, 1, 1, 1, 2, 0, 1, 3, 0, 1, 1, 4, 0, 3, 0, 1, 5, 0, 6, 0, 0, 1, 6, 0, 10, 0, 0, 0, 1, 7, 0, 15, 0, 0, 0, 1, 1, 8, 0, 21, 0, 0, 0, 4, 0, 1, 9, 0, 28, 0, 0, 0, 10, 0, 0, 1, 10, 0, 36, 0, 0, 0, 20, 0, 0, 0, 1, 11, 0, 45, 0, 0, 0, 35, 0, 0, 0, 0, 1, 12, 0, 55, 0, 0, 0, 56, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS First row of the array = the Fredholm-Rueppel sequence (A036987); which becomes the right border of the triangle. Second row of the array (1, 2, 0, 3, 0, 0, 0, 4,...) = A104117. Third row of the array (1, 3, 0, 6, 0, 0, 0, 10,...) = A129502. Row sums of triangle A129503 = A129504: (1, 2, 3, 5, 8, 12, 17, 24, 34,...). LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 FORMULA Antidiagonals of an array in which n-th row (n=0,1,2,...) = M^n * V, where M = A115361 as an infinite lower triangular matrix and V = the Fredholm-Rueppel sequence A036987 as a vector: [1, 1, 0, 1, 0, 0, 0, 1,...]. The array = 1, 1, 0, 1, 0, 0, 0, 1, 0,... 1, 2, 0, 3, 0, 0, 0, 4, 0,... 1, 3, 0, 6, 0, 0, 0, 10, 0,... 1, 4, 0, 10, 0, 0, 0, 20, 0,... .. (n+1)-th row can be generated from A115361 * n-th row. T(n, 2^e) = binomial(n + e - 2^e, e), T(n, k) = 0 otherwise. - Andrew Howroyd, Aug 09 2018 EXAMPLE First few rows of the triangle are: 1; 1,  1; 1,  2, 0; 1,  3, 0,  1; 1,  4, 0,  3, 0; 1,  5, 0,  6, 0, 0; 1,  6, 0, 10, 0, 0, 0; 1,  7, 0, 15, 0, 0, 0,  1; 1,  8, 0, 21, 0, 0, 0,  4, 0; 1,  9, 0, 28, 0, 0, 0, 10, 0, 0; 1, 10, 0, 36, 0, 0, 0, 20, 0, 0, 0; ... PROG (PARI) T(n, k)=my(e=valuation(k, 2)); if(k==2^e, binomial(n-k+e, e)) \\ Andrew Howroyd, Aug 09 2018 CROSSREFS Row sums are A129504. Cf. A036987, A115361, A104117, A129502. Sequence in context: A278045 A096335 A191910 * A225682 A144185 A143987 Adjacent sequences:  A129500 A129501 A129502 * A129504 A129505 A129506 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Apr 18 2007 EXTENSIONS a(53) corrected and terms a(67) and beyond from Andrew Howroyd, Aug 09 2018 STATUS approved

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Last modified January 22 16:27 EST 2020. Contains 331152 sequences. (Running on oeis4.)