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A014736 Squares of odd triangular numbers. 2
1, 9, 225, 441, 2025, 3025, 8281, 11025, 23409, 29241, 53361, 64009, 105625, 123201, 189225, 216225, 314721, 354025, 494209, 549081, 741321, 815409, 1071225, 1168561, 1500625, 1625625, 2047761, 2205225, 2732409, 2927521 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = A014493(n+1)^2. - Vincenzo Librandi, Mar 23 2012

From G. C. Greubel, Jul 24 2019: (Start)

G.f.: x*(1 + 8*x + 212*x^2 + 184*x^3 + 726*x^4 + 184*x^5 + 212*x^6 + 8*x^7 + x^8)/((1 - x)^5*(1 + x)^4).

E.g.f.: (1 + x + 5*x^2 + 20*x^3 + 4*x^4)*cosh(x) - x*(1 - 17*x - 12*x^2 - 4*x^3)* sinh(x) - 1. (End)

MATHEMATICA

Select[Accumulate[Range[70]], OddQ]^2 (* Harvey P. Dale, Mar 22 2012 *)

PROG

(MAGMA) [((2*n-1)*(2*n-1-(-1)^n))^2/4: n in [1..30]]; // Vincenzo Librandi, Mar 23 2012

(PARI) vector(30, n, ((2*n-1)*(2*n-1-(-1)^n))^2/4) \\ G. C. Greubel, Jul 24 2019

(Sage) [((2*n-1)*(2*n-1-(-1)^n))^2/4 for n in (1..30)] # G. C. Greubel, Jul 24 2019

(GAP) List([1..30], n-> ((2*n-1)*(2*n-1-(-1)^n))^2/4); # G. C. Greubel, Jul 24 2019

(Scala) ((1 to 78).scanLeft(0)(_ + _)).filter(_ % 2 == 1).map(n => n * n) // Alonso del Arte, Jul 24 2019

CROSSREFS

Cf. A000217, A014493.

Sequence in context: A036896 A120319 A057530 * A017558 A159939 A167038

Adjacent sequences:  A014733 A014734 A014735 * A014737 A014738 A014739

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

More terms from James A. Sellers

STATUS

approved

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Last modified October 22 03:04 EDT 2019. Contains 328315 sequences. (Running on oeis4.)