A106229
Least j > 1 for n > 0 such that j^2 = (n^2 + 1)*(k^2) + (n^2 + 1)*k + 1 where k sequence = A106230.
Original entry on oeis.org
5, 19, 11, 35, 79, 149, 251, 391, 575, 809, 1099, 1451, 1871, 2365, 2939, 3599, 4351, 5201, 6155, 7219, 8399, 9701, 11131, 12695, 14399, 16249, 18251, 20411, 22735, 25229, 27899, 30751, 33791, 37025, 40459, 44099, 47951, 52021, 56315, 60839, 65599, 70601, 75851
Offset: 1
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LinearRecurrence[{4,-6,4,-1},{5,19,11,35,79,149},43] (* Georg Fischer, Oct 25 2020 *)
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a(n) = if(n<3, 14*n-9, n^3-2*n^2+n-1); \\ Jinyuan Wang, Apr 07 2020
A128888
Table with g.f. [1-x*n-sqrt(x^2*n^2-2*n*x+1+4*x^2-4*x)]/(2*x).
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 10, 0, 1, 4, 15, 36, 36, 0, 1, 5, 24, 84, 176, 137, 0, 1, 6, 35, 160, 510, 912, 543, 0, 1, 7, 48, 270, 1152, 3279, 4928, 2219, 0, 1, 8, 63, 420, 2240, 8768, 21975, 27472, 9285, 0, 1, 9, 80, 616, 3936, 19605, 69504, 151905, 156864
Offset: 0
Table with rows n>=0 and columns m>=0 starts
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 3, 10, 36, 137, 543, 2219, 9285, 39587, 171369, ...
1, 2, 8, 36, 176, 912, 4928, 27472, 156864, 912832, 5394176, ...
1, 3, 15, 84, 510, 3279, 21975, 151905, 1075425, 7758777, 56839965, ...
1, 4, 24, 160, 1152, 8768, 69504, 568064, 4753920, 40537088, 350963712, ...
1, 5, 35, 270, 2240, 19605, 178535, 1675495, 16095765, 157527055, 1565170985, ...
1, 6, 48, 420, 3936, 38832, 398208, 4205904, 45459840, 500488512, 5593373184, ...
1, 7, 63, 616, 6426, 70427, 801423, 9387917, 112501809, 1372985957, 17007257421,...
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H := proc(n,x) (-x*n+1-(x^2*n^2-2*n*x+1+4*x^2-4*x)^(1/2))/(2*x) ; end: T := proc(n,m) coeftayl( H(n,x),x=0,m) ; end: for diag from 0 to 20 do for m from 0 to diag do n := diag-m ; printf("%d, ",T(n,m)) ; od ; od;
Showing 1-2 of 2 results.
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