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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 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.)