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A073371 Convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0 with itself. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

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

LINKS

Table of n, a(n) for n=0..29.

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

FORMULA

a(n) = sum(b(k) * b(n-k), k=0..n) with b(k) := A001045(k+1).

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

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

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

MATHEMATICA

Table[((6n + 4)/27)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)

CROSSREFS

Second (m=1) column of triangle A073370.

Cf. 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

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Last modified December 14 01:22 EST 2019. Contains 329978 sequences. (Running on oeis4.)