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A097038 A Jacobsthal variant. 2
0, 1, 1, 5, 7, 21, 35, 85, 155, 341, 651, 1365, 2667, 5461, 10795, 21845, 43435, 87381, 174251, 349525, 698027, 1398101, 2794155, 5592405, 11180715, 22369621, 44731051, 89478485, 178940587, 357913941, 715795115, 1431655765, 2863245995 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Convolution of A001045 and A077957.

Also interleaving of A002450(n+1) and A006095(n+1).

LINKS

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (1,4,-2,-4).

FORMULA

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

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

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

a(n) = sum{k=0..n, 2^(k/2)(1+(-1)^k)A001045(n-k)/2 };

a(n) = A001045(n+1)-A077957(n).

PROG

(PARI) concat(0, Vec(x/((1-2*x^2)*(1-x-2*x^2)) + O(x^50))) \\ Michel Marcus, Nov 13 2015

(PARI) vector(50, n, n--; 2*2^n/3+(-1)^n/3-2^(n/2)*(1+(-1)^n)/2) \\ Altug Alkan, Nov 13 2015

CROSSREFS

Cf. A001045, A077957.

Cf. A002450, A006095.

Sequence in context: A076197 A002596 A098597 * A049114 A179189 A030735

Adjacent sequences:  A097035 A097036 A097037 * A097039 A097040 A097041

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 19 2004

STATUS

approved

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Last modified February 18 23:16 EST 2018. Contains 299330 sequences. (Running on oeis4.)