A140113 - OEIS

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A140113

a(1)=1, a(n)=a(n-1)+n if n odd, a(n)=a(n-1)+ n^2 if n is even.

1, 5, 8, 24, 29, 65, 72, 136, 145, 245, 256, 400, 413, 609, 624, 880, 897, 1221, 1240, 1640, 1661, 2145, 2168, 2744, 2769, 3445, 3472, 4256, 4285, 5185, 5216, 6240, 6273, 7429, 7464, 8760, 8797, 10241, 10280, 11880, 11921, 13685, 13728, 15664, 15709

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OFFSET

1,2

COMMENTS

One notices the powers 8, 256, 400, and 2744 (14^3) and wonders if the sum is ever again a power. [J. M. Bergot, Sep 07 2011]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

FORMULA

O.g.f.: (-x^4 + 4*x^3 + 4*x + 1)/(x^7 - x^6 - 3*x^5 + 3*x^4 + 3*x^3 - 3*x^2 - x + 1). - Alexander R. Povolotsky, May 08 2008

a(2*n) = A185872(n,2); a(2*n-1) = A100178(n). - Franck Maminirina Ramaharo, Feb 26 2018

MATHEMATICA

nxt[{n_, a_}]:={n+1, If[EvenQ[n], a+n+1, a+(n+1)^2]}; Transpose[ NestList[ nxt, {1, 1}, 50]][[2]] (* or *) LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 5, 8, 24, 29, 65, 72}, 50] (* Harvey P. Dale, Jul 22 2014 *)

CoefficientList[Series[(- x^4 + 4 x^3 + 4 x + 1)/(x^7 - x^6 - 3 x^5 + 3 x^4 + 3 x^3 - 3 x^2 - x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 23 2014 *)

PROG

(PARI) print1(a=1); for(n=2, 99, print1(", ", a+=n^(2-n%2))) \\ Charles R Greathouse IV, Jul 19 2011

CROSSREFS

Cf. A136047.

Sequence in context: A169701 A271008 A272577 * A357117 A368484 A346552

Adjacent sequences: A140110 A140111 A140112 * A140114 A140115 A140116

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, May 08 2008

STATUS

approved