A073371 Convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n >= 0, with itself.

1, 2, 7, 16, 41, 94, 219, 492, 1101, 2426, 5311, 11528, 24881, 53398, 114083, 242724, 514581, 1087410, 2291335, 4815680, 10097401, 21126862, 44117867, 91963996, 191384541, 397682154, 825190479, 1710033272, 3539371201, 7317351686

Offset

0,2

Comments

PSumSIGN transform of A045883(n-1). - Michael Somos, Jul 10 2003

Numbers of the form ((6*m+4)*2^m + (-1)^(m-1)*(3*m+4))/27. - Artur Jasinski, Feb 09 2007

With [0, 0, 0] prepended, this is an "autosequence" of the first kind, whose companion is [0, 0, 2, 3, 12, 25, 66, ...], that is A099429. - Jean-François Alcover, Jul 10 2022

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Wieb Bosma, Signed bits and fast exponentiation, J. Th. Nombres de Bordeaux, 13 no. 1 (2001), p. 27-41.

OEIS Wiki, Autosequence

Formula

a(n) = Sum_{k=0..n} b(k) * b(n-k), where b(k) = A001045(k+1).

a(n) = Sum_{k=0..floor(n/2)} (n-k+1) * binomial(n-k, k) * 2^k.

a(n) = ((n+1)*U(n+1) + 4*(n+2)*U(n))/9 with U(n) = A001045(n+1), n>=0.

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

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

a(n) = ((5+3*n)*2^(n+2) + (7+3*n)*(-1)^n)/27.

a(n) = ((6*n+4)*2^(n) + (-1)^(n-1)*(3*n+4))/27. - Artur Jasinski, Feb 09 2007

E.g.f.: (1/27)*(4*(5+6*x)*exp(2*x) + (7-3*x)*exp(-x)). - G. C. Greubel, Sep 28 2022

Mathematica

Table[((6n+4)*2^n + (-1)^(n-1)(3n+4))/27, {n, 100}] (* Artur Jasinski, Feb 09 2007 *)

Prog

(PARI) a(n) = if(n<-3, 0, ((5+3*n)*2^(n+2)+(7+3*n)*(-1)^n)/27)
(Magma) [((5+3*n)*2^(n+2) + (-1)^n*(7+3*n))/27: n in [0..40]]; // G. C. Greubel, Sep 28 2022
(SageMath)
def A073371(n): return ((5+3*n)*2^(n+2) + (-1)^n*(7+3*n))/27
[A073371(n) for n in range(40)] # G. C. Greubel, Sep 28 2022

Crossrefs

Second (m=1) column of triangle A073370.

Cf. A001045, A062111, A099429, A127976.

Sequence in context: A065497 A131727 A320236 * A113224 A178945 A309561

Adjacent sequences: A073368 A073369 A073370 * A073372 A073373 A073374

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007

Status

approved