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A123490 Triangle whose k-th column satisfies a(n) = (k+3)*a(n-1)-(k+2)*a(n-2). 3
1, 2, 1, 4, 2, 1, 8, 5, 2, 1, 16, 14, 6, 2, 1, 32, 41, 22, 7, 2, 1, 64, 122, 86, 32, 8, 2, 1, 128, 365, 342, 157, 44, 9, 2, 1, 256, 1094, 1366, 782, 260, 58, 10, 2, 1, 512, 3281, 5462, 3907, 1556, 401, 74, 11, 2, 1, 1024, 9842, 21846, 19532, 9332, 2802, 586, 92, 12, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
Column k has g.f.: x^k*(1-x(1+k))/((1-x)*(1-x(2+k))).
T(n,k) = ((k+2)^(n-k) + k)/(k+1), for 0 <= k <= n.
Sum_{k=0..n} T(n, k) = A103439(n+1).
Sum_{k=0..floor(n/2)} T(n-k, k) = A123491(n).
EXAMPLE
Triangle begins
1;
2, 1;
4, 2, 1;
8, 5, 2, 1;
16, 14, 6, 2, 1;
32, 41, 22, 7, 2, 1;
64, 122, 86, 32, 8, 2, 1;
128, 365, 342, 157, 44, 9, 2, 1;
256, 1094, 1366, 782, 260, 58, 10, 2, 1;
512, 3281, 5462, 3907, 1556, 401, 74, 11, 2, 1;
1024, 9842, 21846, 19532, 9332, 2802, 586, 92, 12, 2, 1;
MATHEMATICA
Table[((k+2)^(n-k) +k)/(k+1), {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 14 2017 *)
PROG
(PARI) for(n=0, 10, for(k=0, n, print1(((k+2)^(n-k)+k)/(k+1), ", "))) \\ G. C. Greubel, Oct 14 2017
(Magma) [((k+2)^(n-k) +k)/(k+1): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 15 2021
(Sage) flatten([[((k+2)^(n-k) +k)/(k+1) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 15 2021
CROSSREFS
Columns include A000079, A007051, A047849, A047850, A047851.
Cf. A047848, A103439 (row sums), A123491 (diagonal sums).
Sequence in context: A228565 A054453 A109433 * A157028 A060637 A123486
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Oct 01 2006
STATUS
approved

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)