A381374 Little Hankel transform of A317614: a(n) = A317614(n+1)^2 - A317614(n)*A317614(n+2).

1, 1, 97, 49, 769, 289, 2977, 961, 8161, 2401, 18241, 5041, 35617, 9409, 63169, 16129, 104257, 25921, 162721, 39601, 242881, 58081, 349537, 82369, 487969, 113569, 663937, 152881, 883681, 201601, 1153921, 261121, 1481857, 332929, 1875169, 418609, 2342017, 519841, 2891041

Offset

1,3

Links

Table of n, a(n) for n=1..39.

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-10,0,10,0,-5,0,1).

Formula

a(n) = (10 + 6*(-1)^n + 4*n*(n + 2)*(3*(n + 1)^2 + (-1)^n*(2*n^2 + 4*n + 5)))/16.

a(n) = 5*a(n-2) - 10*a(n-4) + 10*a(n-6) - 5*a(n-8) + a(n-10) for n > 10.

G.f.: (1 + x + 92*x^2 + 44*x^3 + 294*x^4 + 54*x^5 + 92*x^6 - 4*x^7 + x^8 + x^9)/(1 - x^2)^5.

E.g.f.: ((4 + 3*x + 123*x^2 + 10*x^3 + 5*x^4)*cosh(x) + (1 + 69*x + 21*x^2 + 50*x^3 + x^4)*sinh(x))/4.

a(2*n) = A239607(n).

Mathematica

LinearRecurrence[{0, 5, 0, -10, 0, 10, 0, -5, 0, 1}, {1, 97, 49, 769, 289, 2977, 961, 8161, 2401, 18241}, 38]

Crossrefs

Cf. A317614.

Cf. A056221, A056222, A239607, A374668.

Sequence in context: A068830 A033417 A182690 * A088866 A244192 A075478

Adjacent sequences: A381369 A381371 A381373 * A381376 A381377 A381378

Keyword

nonn,easy,new

Author

Stefano Spezia, Feb 21 2025

Status

approved