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A276764
1^2 + 3^2, 2^2 + 4^2, 5^2 + 7^2, 6^2 + 8^2, ...
1
10, 20, 74, 100, 202, 244, 394, 452, 650, 724, 970, 1060, 1354, 1460, 1802, 1924, 2314, 2452, 2890, 3044, 3530, 3700, 4234, 4420, 5002, 5204, 5834, 6052, 6730, 6964, 7690, 7940, 8714, 8980, 9802, 10084, 10954, 11252, 12170, 12484, 13450, 13780, 14794, 15140
OFFSET
1,1
FORMULA
a(n) = (2n - 1 - ((n+1) mod 2))^2 + (2n + (n mod 2))^2.
From Colin Barker, Nov 10 2016: (Start)
G.f.: 2*x*(5 + 5*x + 17*x^2 + 3*x^3 + 2*x^4) / ((1 - x)^3 * (1 + x)^2).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5.
a(n) = 8*n^2 - 8*n + 4 for n even.
a(n) = 8*n^2 + 2 for n odd.
(End)
MATHEMATICA
LinearRecurrence[{1, 2, -2, -1, 1}, {10, 20, 74, 100, 202}, 50] (* Harvey P. Dale, Mar 02 2023 *)
PROG
(PARI) Vec(2*x*(5+5*x+17*x^2+3*x^3+2*x^4) / ((1-x)^3*(1+x)^2) + O(x^60)) \\ Colin Barker, Nov 10 2016
CROSSREFS
Cf. A001844.
Sequence in context: A337434 A328490 A131726 * A215878 A200985 A375232
KEYWORD
nonn,easy
AUTHOR
Edwin McCravy, Nov 06 2016
STATUS
approved