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A262491
The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of eleven consecutive positive triangular numbers.
4
43, 120, 549, 3783, 17214, 47629, 216688, 1490884, 6782665, 18766098, 85374915, 587404905, 2672353188, 7393795375, 33637500214, 231436042078, 1052900373799, 2913136612044, 13253089709793, 91185213174219, 414840074924010, 1147768431350353, 5221683708158620
OFFSET
1,1
COMMENTS
For the index of the first of the corresponding eleven consecutive triangular numbers, see A116476.
FORMULA
G.f.: -x*(10*x^8+33*x^6+77*x^5-3511*x^4+3234*x^3+429*x^2+77*x+43) / ((x-1)*(x^8-394*x^4+1)).
EXAMPLE
43 is in the sequence because T(43)+T(44) = 946+990 = 1936 = 91+...+276 = T(13)+...+T(23), where T(k) is the k-th triangular number.
MATHEMATICA
LinearRecurrence[{1, 0, 0, 394, -394, 0, 0, -1, 1}, {43, 120, 549, 3783, 17214, 47629, 216688, 1490884, 6782665}, 30] (* Harvey P. Dale, May 17 2020 *)
PROG
(PARI) Vec(-x*(10*x^8+33*x^6+77*x^5-3511*x^4+3234*x^3+429*x^2+77*x+43)/((x-1)*(x^8-394*x^4+1)) + O(x^30))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Sep 24 2015
STATUS
approved