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

Author

Paul D. Hanna, Jul 29 2002

Keywords

• easy
• nonn
• tabl

Examples

			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.

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).

Extensions

Formulas simplified by Paul D. Hanna, Nov 26 2012

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