login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A252630 Numbers n such that the sum of the hexagonal numbers X(n), X(n+1), X(n+2) and X(n+3) is equal to the heptagonal number H(m) for some m. 2
50, 16503, 5314316, 1711193649, 550999041062, 177419980028715, 57128682570205568, 18395258367626164581, 5923216065693054789914, 1907257177894796016188127, 614130888066058624157787380, 197748238700092982182791348633, 63674318730541874204234656472846 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also positive integers x in the solutions to 16*x^2-5*y^2+40*x+3*y+44 = 0, the corresponding values of y being A252631.

LINKS

Colin Barker, Table of n, a(n) for n = 1..398

Index entries for linear recurrences with constant coefficients, signature (323,-323,1).

FORMULA

a(n) = 323*a(n-1)-323*a(n-2)+a(n-3).

G.f.: x*(3*x^2-353*x-50) / ((x-1)*(x^2-322*x+1)).

a(n) =-5/4+1/80*(161+72*sqrt(5))^(-n)*(-70-37*sqrt(5)+(-70+37*sqrt(5))*(161+72*sqrt(5))^(2*n)). - Colin Barker, Mar 03 2016

EXAMPLE

50 is in the sequence because X(50)+X(51)+X(52)+X(53) = 4950+5151+5356+5565 = 21022 = H(92).

PROG

(PARI) Vec(x*(3*x^2-353*x-50)/((x-1)*(x^2-322*x+1)) + O(x^100))

CROSSREFS

Cf. A000384, A000566, A252631.

Sequence in context: A152258 A203097 A028465 * A034205 A173170 A146518

Adjacent sequences:  A252627 A252628 A252629 * A252631 A252632 A252633

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Dec 19 2014

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 14:52 EST 2020. Contains 338769 sequences. (Running on oeis4.)