A262490
The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of four consecutive positive triangular numbers.
Original entry on oeis.org
9, 57, 337, 1969, 11481, 66921, 390049, 2273377, 13250217, 77227929, 450117361, 2623476241, 15290740089, 89120964297, 519435045697, 3027489309889, 17645500813641, 102845515571961, 599427592618129, 3493720040136817, 20362892648202777, 118683635849079849
Offset: 1
9 is in the sequence because T(9)+T(10) = 45+55 = 100 = 15+21+28+36 = T(5)+T(6)+T(7)+T(8), where T(k) is the k-th triangular number.
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.
Original entry on oeis.org
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
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.
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,394,-394,0,0,-1,1).
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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 *)
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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))
A262492
The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of thirteen consecutive positive triangular numbers.
Original entry on oeis.org
25, 90, 207, 1117, 2560, 9255, 21202, 114022, 261195, 944020, 2162497, 11629227, 26639430, 96280885, 220553592, 1186067232, 2716960765, 9819706350, 22494303987, 120967228537, 277103358700, 1001513766915, 2294198453182, 12337471243642, 28261825626735
Offset: 1
25 is in the sequence because T(25)+T(26) = 325+351 = 676 = 6+...+120 = T(3)+...+T(15), where T(k) is the k-th triangular number.
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,102,-102,0,0,-1,1).
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