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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

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

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.

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, 10}, {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

CROSSREFS

Columns include A000079, A007051, A047849, A047850, A047851.

Row sums are A103439.

Diagonal sums are A123491.

Cf. A047848.

Sequence in context: A228565 A054453 A109433 * A157028 A060637 A123486

Adjacent sequences:  A123487 A123488 A123489 * A123491 A123492 A123493

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 01 2006

STATUS

approved

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Last modified June 4 11:32 EDT 2020. Contains 334825 sequences. (Running on oeis4.)