A073153 Triangle of numbers relating two sequences A073155 and A073156.

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, 7540, 8324, 9272, 10318, 15080, 22198, 26960, 31144, 34462, 37598, 40916, 45100, 49862, 72060, 105430, 127628

Offset

0,3

Links

Table of n, a(n) for n=0..46.

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 A362609 A238656

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

a(31) onward corrected by Sean A. Irvine, Nov 18 2024

Status

approved