A048470 - OEIS

A048470

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

1, 3, 9, 26, 70, 177, 427, 996, 2268, 5075, 11209, 24510, 53170, 114597, 245655, 524168, 1113976, 2359143, 4980565, 10485570, 22019886, 46137113, 96468739, 201326316, 419430100, 872414907, 1811938977, 3758096006, 7784627818

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OFFSET

0,2

COMMENTS

a(n) = T(0,n) + T(1,n-1) + ... + T(n,0), array T given by A047858.

Sum of the consecutive integers from 2^n-n up to and including 2^n. - J. M. Bergot, Jun 27 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: (-1 + 5*x^3 - 7*x^2 + 4*x)/((2*x-1)^2*(x-1)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 13 2009

a(n) = 3^n - Eulerian(n,2) = A000244(n) - A000460(n). - Peter Luschny, May 13 2016

PROG

(Magma) [(n+1)*(2^(n+1)-n)/2: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011

(PARI) a(n)=(n+1)*(2<<n-n)/2 \\ Charles R Greathouse IV, Jun 28 2013

CROSSREFS

Sequence in context: A258097 A221946 A291410 * A138237 A121286 A072863

Adjacent sequences: A048467 A048468 A048469 * A048471 A048472 A048473

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Edited by T. D. Noe, Dec 11 2006

STATUS

approved