login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A133100 Expansion of f(x, x^4) in powers of x where f(, ) is Ramanujan's general theta function. 8
1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for characteristic functions

FORMULA

f(x,x^m) = 1 + Sum_k=1..oo} x^((m+1)*k*(k-1)/2) (x^k + x^(m*k)). - N. J. A. Sloane, Jan 30 2017

The characteristic function of A085787 generalized heptagonal numbers.

Euler transform of period 10 sequence [1, -1, 0, 1, -1, 1, 0, -1, 1, -1, ...].

G.f.: Prod_{k>0} (1 - x^(5*k)) * (1 + x^(5*k - 1)) * (1 + x^(5*k - 4)) = Sum_{k in Z} x^((5*k^2 + 3*k) / 2).

a(n) = |A113429(n)|. a(3*n + 2) = 0.

EXAMPLE

G.f. = 1 + x + x^4 + x^7 + x^13 + x^18 + x^27 + x^34 + x^46 + x^55 + x^70 + ...

G.f. = q^9 + q^49 + q^169 + q^289 + q^529 + q^729 + q^1089 + q^1369 + q^1849 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^5] QPochhammer[ -x^4, x^5] QPochhammer[ x^5], {x, 0, n}]; (* Michael Somos, Oct 31 2015 *)

a[ n_] := SquaresR[ 1, 40 n + 9] / 2; (* Michael Somos, Jan 30 2017 *)

a[ n_] := If[n < 0, 0, Boole @ IntegerQ @ Sqrt @ (40 n + 9)]; (* Michael Somos, Jan 30 2017 *)

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( prod( k=1, n, 1 + x^k*[-1, 1, 0, 0, 1][k%5 + 1], 1 + x * O(x^n)), n))};

(PARI) {a(n) = issquare( 40*n + 9)};

CROSSREFS

Cf. f(x, x^k) for k=2..11: A080995, A010054, A133100, A089801, A274179, A214263, A281814, A205988, A281815, A186742.

Cf. A085787, A113429.

Sequence in context: A087049 A118009 A113429 * A216230 A077606 A004601

Adjacent sequences:  A133097 A133098 A133099 * A133101 A133102 A133103

KEYWORD

nonn

AUTHOR

Michael Somos, Sep 11 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 21 12:54 EST 2018. Contains 299411 sequences. (Running on oeis4.)