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A299921 Squares that differ from a triangular number by 1. 4
0, 1, 4, 9, 16, 121, 324, 529, 4096, 11025, 17956, 139129, 374544, 609961, 4726276, 12723489, 20720704, 160554241, 432224100, 703893961, 5454117904, 14682895929, 23911673956, 185279454481, 498786237504, 812293020529, 6294047334436, 16944049179225, 27594051024016 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Squares k such that 8*k-7 or 8*k+9 is a square. - Robert Israel, Mar 18 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..1959

Index entries for linear recurrences with constant coefficients, signature (0,0,35,0,0,-35,0,0,1).

FORMULA

From Robert Israel, Mar 18 2018: (Start)

G.f.: x^2*(1+4*x+9*x^2-19*x^3-19*x^4+9*x^5+4*x^6+x^7)/(1-35*x^3+35*x^6-x^9).

a(n) = 35*a(n-3) - 35*a(n-6) + a(n-9). (End)

MAPLE

f:= gfun:-rectoproc({a(n+9) = 35*a(n+6) - 35*a(n+3) + a(n), seq(a(i)=[0, 1, 4, 9, 16, 121, 324, 529, 4096][i], i=1..9)}, a(n), remember):

map(f, [$1..50]); # Robert Israel, Mar 18 2018

PROG

(PARI) isok(n) = issquare(n) && (ispolygonal(n+1, 3) || ispolygonal(n-1, 3)); \\ Michel Marcus, Mar 17 2018

CROSSREFS

Cf. A001110, A164080, A182334, A229131.

Sequence in context: A038239 A263094 A226354 * A089149 A082920 A204434

Adjacent sequences:  A299918 A299919 A299920 * A299922 A299923 A299924

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 17 2018

EXTENSIONS

More terms from Altug Alkan, Mar 17 2018

STATUS

approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)