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A193673 Triangle given by p(n,k)=(coefficient of x^(n-k) in (1/2) ((x+3)^n+(x+1)^n)), 0<=k<=n. 2
1, 2, 1, 5, 4, 1, 14, 15, 6, 1, 41, 56, 30, 8, 1, 122, 205, 140, 50, 10, 1, 365, 732, 615, 280, 75, 12, 1, 1094, 2555, 2562, 1435, 490, 105, 14, 1, 3281, 8752, 10220, 6832, 2870, 784, 140, 16, 1, 9842, 29529, 39384, 30660, 15372, 5166, 1176, 180, 18, 1, 29525 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..55.

EXAMPLE

First five rows:

1

2...1

5...4...1

14..15..6...1

41..56..30..8..1

MATHEMATICA

q[n_, k_] := 1; r[0] = 1;

r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}]

p[n_, k_] := Coefficient[(1/2) ((x + 3)^n + (x + 1)^n), x, k] (* A193673 *)

v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]

Table[v[n], {n, 0, 20}]    (* A193661 *)

TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]

Table[r[k], {k, 0, 8}]  (* 2^k *)

TableForm[Table[p[n, k], {n, 0, 10}, {k, 0, n}]] (* A193673 as a triangle *)

Flatten[%] (* A193673 as a sequence *)

CROSSREFS

Cf. A193661.

Sequence in context: A104710 A039598 A128738 * A126181 A154930 A104259

Adjacent sequences:  A193670 A193671 A193672 * A193674 A193675 A193676

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 02 2011

STATUS

approved

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Last modified December 5 15:24 EST 2016. Contains 278770 sequences.