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A024381 a(n) = sum of squares of first n positive integers congruent to 1 mod 4. 1
1, 26, 107, 276, 565, 1006, 1631, 2472, 3561, 4930, 6611, 8636, 11037, 13846, 17095, 20816, 25041, 29802, 35131, 41060, 47621, 54846, 62767, 71416, 80825, 91026, 102051, 113932, 126701, 140390, 155031, 170656, 187297, 204986, 223755, 243636, 264661 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

1^2 + 5^2 + 9^2 + ... + (4n+1)^2 = (4n+1)(n+1)+(4^2)(2n+1)(n+1)n/6, which generalizes to (0a+1)^2 + (1a+1)^2 + (2a+1)^2 + ... + (na+1)^2 = (an+1)(n+1) + (a^2)(2n+1)(n+1)n/6. Also Sum{n}_(an+1)^2 = (an+1)(n+1) + (a^2)* sum{n}_(n+1)^2. - Helmut Rasinger (helmut.rasinger(AT)wanadoo.fr), Sep 04 2003

G.f.:  x*(1 + 22*x + 9*x^2) /  (x-1)^4. - R. J. Mathar, Oct 08 2011

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 19 2012

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {1, 26, 107, 276}, 40] (* Vincenzo Librandi, Jun 19 2012 *)

Accumulate[Range[1, 151, 4]^2] (* Harvey P. Dale, Apr 25 2020 *)

PROG

(MAGMA) I:=[1, 26, 107, 276]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 19 2012

CROSSREFS

Sequence in context: A042324 A044277 A044658 * A262756 A262476 A156385

Adjacent sequences:  A024378 A024379 A024380 * A024382 A024383 A024384

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified November 26 19:27 EST 2020. Contains 338641 sequences. (Running on oeis4.)