The On-Line Encyclopedia of Integer Sequences (OEIS)

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A253476

Indices of centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).
(history; published version)

#12 by Harvey P. Dale at Tue Jun 14 09:07:13 EDT 2016

STATUS

editing

approved

#11 by Harvey P. Dale at Tue Jun 14 09:07:07 EDT 2016

MATHEMATICA

LinearRecurrence[{1, 110, -110, -1, 1}, {1, 15, 70, 1596, 7645}, 30] (* Harvey P. Dale, Jun 14 2016 *)

STATUS

approved

editing

#10 by Charles R Greathouse IV at Sat Jun 13 00:55:21 EDT 2015

LINKS

<a href="/index/Rec#order_05">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,110,-110,-1,1).

Discussion

Sat Jun 13

00:55

OEIS Server: https://oeis.org/edit/global/2439

#9 by Joerg Arndt at Fri Jan 09 07:12:05 EST 2015

STATUS

proposed

approved

#8 by Colin Barker at Fri Jan 09 06:58:02 EST 2015

STATUS

editing

proposed

#7 by Colin Barker at Fri Jan 09 06:57:55 EST 2015

CROSSREFS

Cf. A005448, A069099, A253477, A253689.

STATUS

approved

editing

#6 by Michel Marcus at Fri Jan 02 11:20:15 EST 2015

STATUS

reviewed

approved

#5 by Joerg Arndt at Fri Jan 02 09:28:45 EST 2015

STATUS

proposed

reviewed

#4 by Colin Barker at Fri Jan 02 08:41:43 EST 2015

STATUS

editing

proposed

#3 by Colin Barker at Fri Jan 02 08:37:14 EST 2015

NAME

allocated for Colin BarkerIndices of centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).

DATA

1, 15, 70, 1596, 7645, 175491, 840826, 19302360, 92483161, 2123084055, 10172306830, 233519943636, 1118861268085, 25685070715851, 123064567182466, 2825124258799920, 13535983528803121, 310737983397275295, 1488835123601160790, 34178353049441482476

OFFSET

1,2

COMMENTS

Also positive integers x in the solutions to 3*x^2 - 7*y^2 - 3*x + 7*y = 0, the corresponding values of y being A253477.

LINKS

Colin Barker, <a href="/A253476/b253476.txt">Table of n, a(n) for n = 1..980</a>

<a href="/index/Rec#order_05">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,110,-110,-1,1).

FORMULA

a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(14*x^3+55*x^2-14*x-1) / ((x-1)*(x^4-110*x^2+1)).

EXAMPLE

15 is in the sequence because the 15th centered triangular number is 316, which is also the 10th centered heptagonal number.

PROG

(PARI) Vec(x*(14*x^3+55*x^2-14*x-1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))

CROSSREFS

Cf. A005448, A069099, A253477.

KEYWORD

allocated

nonn,easy

AUTHOR

Colin Barker, Jan 02 2015

STATUS

approved

editing