A131913 Product of the square matrix in A065941 and the column vector (1, 2, 3, ...)'.

1, 3, 6, 13, 25, 48, 89, 163, 294, 525, 929, 1632, 2849, 4947, 8550, 14717, 25241, 43152, 73561, 125075, 212166, 359133, 606721, 1023168, 1722625, 2895843, 4861254, 8149933, 13646809, 22825200, 38136089, 63653827, 106146534, 176849517, 294401825, 489706272

Offset: 0

Author

Gary W. Adamson, Jul 27 2007

Keywords

• nonn
• easy

Examples

			a(4) = 25 = (1, 1, 3, 2, 1) dot (1, 2, 3, 4, 5) = (1 + 2 + 9 + 8 + 5), where (1, 1, 3, 2, 1) = row 4 of triangle A065941.
a(4) = 25 = A010049(4) + A001629(6) = 5 + 20.
a(5) = 48 = A055244(6) + A001629(4) = 43 + 5.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).

Crossrefs

Cf. A000045, A065941, A010049, A001629, A055244.

Formula

a(n) = A010049(n) + A001629(n+2) = A055244(n+1) + A001629(n-1).

From Philippe Deléham, Dec 28 2013: (Start)

G.f.: (1+x-x^2)/(1-x-x^2)^2.

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4), a(0)=1, a(1)=3, a(2)=6, a(3)=13.

a(n) = a(n-1) + a(n-2) + 2*Fibonacci(n). (End)