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A251867 Numbers n such that n^2 + (n+1)^2 is equal to the sum of the hexagonal numbers H(m) and H(m+1) for some m. 2
0, 14, 492, 16730, 568344, 19306982, 655869060, 22280241074, 756872327472, 25711378892990, 873430010034204, 29670908962269962, 1007937474707144520, 34240203231080643734, 1163158972382034742452, 39513164857758100599650, 1342284446191393385645664 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also nonnegative integers y in the solutions to 4*x^2-2*y^2+2*x-2*y = 0, the corresponding values of x being A220185.
LINKS
FORMULA
a(n) = 35*a(n-1)-35*a(n-2)+a(n-3).
G.f.: -2*x^2*(x+7) / ((x-1)*(x^2-34*x+1)).
a(n) = A220185(n) + A001542(n-1)^2. - Alexander Samokrutov, Sep 05 2015
a(n) = (-4+(10+7*sqrt(2))*(17+12*sqrt(2))^(-n)+(10-7*sqrt(2))*(17+12*sqrt(2))^n)/8. - Colin Barker, Mar 02 2016
a(n) = A105635(4*n-4). - Greg Dresden, Aug 30 2021
EXAMPLE
14 is in the sequence because 14^2+15^2 = 196+225 = 421 = 190+231 = H(10)+H(11).
MATHEMATICA
LinearRecurrence[{35, -35, 1}, {0, 14, 492}, 20] (* Vincenzo Librandi, Sep 06 2015 *)
PROG
(PARI) concat(0, Vec(-2*x^2*(x+7)/((x-1)*(x^2-34*x+1)) + O(x^100)))
(Magma) I:=[0, 14, 492]; [n le 3 select I[n] else 35*Self(n-1)-35*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Sep 06 2015
CROSSREFS
Sequence in context: A317635 A128051 A217337 * A240411 A024299 A190999
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Dec 10 2014
STATUS
approved

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Last modified May 20 08:05 EDT 2024. Contains 372703 sequences. (Running on oeis4.)