A117902 -id:A117902 - cp's OEIS frontend

A133464 a(3n)=4^n, a(3n+1)=24^n, a(3n+2)=34^n.

1, 2, 3, 4, 8, 12, 16, 32, 48, 64, 128, 192, 256, 512, 768, 1024, 2048, 3072, 4096, 8192, 12288, 16384, 32768, 49152, 65536, 131072, 196608, 262144, 524288, 786432, 1048576, 2097152, 3145728, 4194304, 8388608, 12582912, 16777216, 33554432

Offset: 0

Paul Curtz, Nov 28 2007

Index entries for linear recurrences with constant coefficients, signature (0,0,4).

Cf. A000079, A037124, A038754, A140730, A140740.

LinearRecurrence[{0,0,4},{1,2,3},40] (* Harvey P. Dale, Jun 07 2012 *)

a(n)=4^(n\3)*(n%3+1) \\ Charles R Greathouse IV, Oct 07 2015

O.g.f.: -(1+2*x+3*x^2)/(-1+4*x^3) . 2*a(n)-a(n+1) = abs(A117902(n+1)). - R. J. Mathar, Nov 30 2007
From Reinhard Zumkeller, May 26 2008: (Start)
a(n+1) = a(n) + a(n - n mod 3).
a(n) = A140740(n+3,3). (End)
Sum_{n>=0} 1/a(n) = 22/9. - Amiram Eldar, Jan 21 2022

Edited by R. J. Mathar, Nov 30 2007

More terms from Reinhard Zumkeller, May 26 2008

A117901 Inverse of number triangle A117898.

Original entry on oeis.org

1, -1, 1, 0, -2, 1, 0, 3, -2, 1, 0, 0, 0, -1, 1, 0, -6, 3, 0, -2, 1, 0, 12, -6, 0, 3, -2, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, -24, 12, 0, -6, 3, 0, -2, 1, 0, 48, -24, 0, 12, -6, 0, 3, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -96, 48, 0, -24, 12, 0, -6, 3, 0, -2, 1, 0, 192, -96, 0, 48, -24, 0, 12, -6, 0, 3, -2, 1

Offset: 0

Paul Barry, Apr 01 2006

Row sums are A117902. Diagonal sums are A117903.

			Triangle begins
1,
-1, 1,
0, -2, 1,
0, 3, -2, 1,
0, 0, 0, -1, 1,
0, -6, 3, 0, -2, 1,
0, 12, -6, 0, 3, -2, 1,
0, 0, 0, 0, 0, 0, -1, 1,
0, -24, 12, 0, -6, 3, 0, -2, 1,
0, 48, -24, 0, 12, -6, 0, 3, -2, 1

G.f.:(2x^6*y^2+x^5*y(2-y)+4x^4(1-y)-x^3(2y^2-3y+4)+x^2*y(y-2)+x(y-1)+1)/((1-4x^3)(1-x^3*y^3))

cp's OEIS Frontend

A133464 a(3n)=4^n, a(3n+1)=24^n, a(3n+2)=34^n.

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A117901 Inverse of number triangle A117898.

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cp's OEIS Frontend

A133464 a(3n)=4^n, a(3n+1)=2*4^n, a(3n+2)=3*4^n.

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A117901 Inverse of number triangle A117898.

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Formula

A133464 a(3n)=4^n, a(3n+1)=24^n, a(3n+2)=34^n.