A224785 Expansion of (1+4*x+8*x^2-x^3)/((1-x)*(1+x)*(1-3*x^2)).

1, 4, 12, 15, 45, 48, 144, 147, 441, 444, 1332, 1335, 4005, 4008, 12024, 12027, 36081, 36084, 108252, 108255, 324765, 324768, 974304, 974307, 2922921, 2922924, 8768772, 8768775, 26306325, 26306328, 78918984, 78918987, 236756961, 236756964, 710270892, 710270895

Offset: 0

Author

Philippe Deléham, Apr 17 2013

Keywords

• nonn
• easy

Comments

A row of the square array A219605.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-3).

Crossrefs

Cf. A219605, A220354.

Programs

GAP

List([0..40], n-> (11*3^Int(n/2) -3*(2+(-1)^n))/2 ); # G. C. Greubel, Nov 12 2019

Magma

[(11*3^Floor(n/2) -3*(2+(-1)^n))/2: n in [0..40]]; // G. C. Greubel, Nov 12 2019

Maple

seq( (11*3^floor(n/2) -3*(2+(-1)^n))/2, n=0..40); # G. C. Greubel, Nov 12 2019

Mathematica

Table[(11*3^Floor[n/2] -3*(2+(-1)^n))/2, {n,0,40}] (* G. C. Greubel, Nov 12 2019 *)

PARI

vector(41, n, (11*3^((n-1)\2) -3*(2-(-1)^n))/2) \\ G. C. Greubel, Nov 12 2019

Sage

[(11*3^floor(n/2) -3*(2+(-1)^n))/2 for n in (0..40)] # G. C. Greubel, Nov 12 2019

Formula

a(n) = a(n-1) + 3 if n odd.

a(n) = 3*a(n-1) if n even.

a(2n) = (11*3^n - 9)/2.

a(2n+1) = (11*3^n - 3)/2.

a(n) = 4*a(n-2) - 3*a(n-4) with n>3, a(0)=1, a(1)=4, a(2)=12, a(3)=15.

a(n) = A219605(3,n).

a(n) = Sum_{k=0..n} A220354(n,k) * 3^k.

a(n) = (11*3^floor(n/2)-3(-1)^n)/2 -3. - Bruno Berselli, Apr 27 2013