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 A291905 Row sums of A291904. 5
 1, 1, 0, 1, 1, 0, 2, 1, 1, 3, 2, 3, 4, 4, 6, 8, 8, 11, 14, 16, 21, 26, 32, 39, 49, 60, 75, 93, 114, 142, 176, 217, 268, 334, 411, 510, 632, 779, 967, 1196, 1477, 1832, 2266, 2801, 3470, 4291, 5310, 6572, 8129, 10061, 12449, 15401, 19058, 23581, 29178, 36102, 44668 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Number of compositions of n where the first part is 1 and the absolute difference between consecutive parts is 1. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 EXAMPLE The a(6)=2 compositions of 6 are: : :  o o| : oooo| : :   o| :  oo| : ooo| : The a(9)=3 compositions of 9 are: : :   o  | :  ooo | : ooooo| : :  o o o| : oooooo| : :     o| :  o oo| : ooooo| MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, add(      `if`(j=i, 0, b(n-j, j)), j=max(1, i-1)..min(i+1, n)))     end: a:= n-> b(n, 0): seq(a(n), n=0..60);  # Alois P. Heinz, Sep 05 2017 MATHEMATICA T[0, 0] = 1; T[_, 0] = 0; T[n_?Positive, k_] /; 0 < k <= Floor[(Sqrt[8n+1] - 1)/2] := T[n, k] = T[n-k, k-1] + T[n-k, k+1]; T[_, _] = 0; a[n_] := Sum[T[n, k], {k, 0, Floor[(Sqrt[8n+1] - 1)/2]}]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, May 29 2019 *) PROG (Python) from sympy.core.cache import cacheit @cacheit def b(n, i): return 1 if n==0 else sum([0 if j==i else b(n - j, j) for j in range(max(1, i - 1), min(i + 1, n) + 1)]) def a(n): return b(n, 0) print(map(a, range(61))) # Indranil Ghosh, Sep 06 2017, after Maple program CROSSREFS Cf. A291896, A291904. Sequence in context: A291874 A049346 A227310 * A240853 A319849 A117334 Adjacent sequences:  A291902 A291903 A291904 * A291906 A291907 A291908 KEYWORD nonn AUTHOR Seiichi Manyama, Sep 05 2017 STATUS approved

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Last modified January 29 11:16 EST 2020. Contains 331337 sequences. (Running on oeis4.)