A195021 a(n) = n*(14*n - 11).

0, 3, 34, 93, 180, 295, 438, 609, 808, 1035, 1290, 1573, 1884, 2223, 2590, 2985, 3408, 3859, 4338, 4845, 5380, 5943, 6534, 7153, 7800, 8475, 9178, 9909, 10668, 11455, 12270, 13113, 13984, 14883, 15810, 16765, 17748, 18759, 19798, 20865, 21960, 23083, 24234, 25413

Offset

0,2

Comments

Sequence found by reading the first two vertices [0, 3] together with the line from 34, in the direction 34, 93, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020, which is related to the primitive Pythagorean triple [3, 4, 5]. For another version see A195030.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 14*n^2 - 11*n.

From Colin Barker, Apr 09 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(3+25*x)/(1-x)^3. (End)

E.g.f.: exp(x)*x*(3 + 14*x). - Elmo R. Oliveira, Dec 30 2024

Prog

(Magma) [14*n^2 - 11*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011
(PARI) a(n)=n*(14*n-11) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A144555, A185019, A193053, A195019, A195020, A195023, A195024, A195025, A195030, A195320, A198017.

Cf. numbers of the form n*(n*k - k + 6)/2, this sequence is the case k=28: see Comments lines of A226492.

Sequence in context: A003348 A344641 A086488 * A344429 A274871 A042041

Adjacent sequences: A195018 A195019 A195020 * A195022 A195023 A195024

Keyword

nonn,easy,changed

Author

Omar E. Pol, Sep 07 2011

Extensions

Edited by Bruno Berselli, Oct 18 2011

Status

approved