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A073153 Triangle of numbers relating two sequences A073155 and A073156. 5
1, 1, 2, 4, 5, 9, 14, 18, 22, 36, 56, 70, 86, 100, 156, 237, 293, 349, 405, 461, 698, 1046, 1283, 1507, 1703, 1927, 2164, 3210, 4762, 5808, 6756, 6980, 7204, 8152, 9198, 13960, 21078 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..36.

FORMULA

Triangle {T(n, k), n >= 0, 0<=k<=n} defined by: T(0, 0)=1,

T(n, 0) = A073155(n), T(n, n) = A073156(n),

T(n, 0) = T(n-1, n-1) + 2*T(n-2, n-2) + T(n-3, n-3),

T(n, k) = Sum_{j=0..k} A073155(j) * A073155(n-j).

EXAMPLE

T(4,0) = T(3,3) + 2*T(2,2) + T(1,1) = 2 + 2*9 + 36 = 56.

T(5,2) = A073155(0)*A073155(5) + A073155(1)*A073155(4) + A073155(2)*A073155(3) = 1*237 + 1*56 + 4*14 = 349.

Triangle begins:

1;

1, 2;

4, 5, 9;

14, 18, 22, 36;

56, 70, 86, 100, 156;

237, 293, 349, 405, 461, 698;

1046, 1283, 1507, 1703, 1927, 2164, 3210; ...

CROSSREFS

Cf. A073154, A073155, A073156, A073157, A073153.

Sequence in context: A126697 A162406 A129282 * A073154 A238656 A077882

Adjacent sequences: A073150 A073151 A073152 * A073154 A073155 A073156

KEYWORD

easy,nonn,tabl

AUTHOR

Paul D. Hanna, Jul 29 2002

EXTENSIONS

Formulas simplified by Paul D. Hanna, Nov 26 2012

STATUS

approved

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Last modified December 6 06:19 EST 2022. Contains 358595 sequences. (Running on oeis4.)