A244630 a(n) = 17*n^2.

0, 17, 68, 153, 272, 425, 612, 833, 1088, 1377, 1700, 2057, 2448, 2873, 3332, 3825, 4352, 4913, 5508, 6137, 6800, 7497, 8228, 8993, 9792, 10625, 11492, 12393, 13328, 14297, 15300, 16337, 17408, 18513, 19652, 20825, 22032, 23273, 24548, 25857, 27200, 28577, 29988

Offset: 0

Author

Vincenzo Librandi, Jul 03 2014

Keywords

• nonn
• easy

Comments

First bisection of A195047. - Bruno Berselli, Jul 03 2014

Norms of purely imaginary numbers in Z[sqrt(-17)] (for example, 3*sqrt(-17) has norm 153). - Alonso del Arte, Jun 23 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A008599, A195047.

Cf. similar sequences of the type k*n^2: A000290 (k = 1), A001105 (k = 2), A033428 (k = 3), A016742 (k = 4), A033429 (k = 5), A033581 (k = 6), A033582 (k = 7), A139098 (k = 8), A016766 (k = 9), A033583 (k = 10), A033584 (k = 11), A135453 (k = 12), A152742 (k = 13), A144555 (k = 14), A064761 (k = 15), A016802 (k = 16), this sequence (k = 17), A195321 (k = 18), A244631 (k = 19), A195322 (k = 20), A064762 (k = 21), A195323 (k = 22), A244632 (k = 23), A195824 (k = 24), A016850 (k = 25), A244633 (k = 26), A244634 (k = 27), A064763 (k = 28), A244635 (k = 29), A244636 (k = 30).

Programs

GAP

List([0..45],n->17*n^2); # Muniru A Asiru, Jun 29 2018

Magma

[17*n^2: n in [0..40]];

Maple

seq(17*n^2,n=0..45); # Muniru A Asiru, Jun 29 2018

Mathematica

Table[17 n^2, {n, 0, 40}]

PARI

a(n)=17*n^2 \\ Charles R Greathouse IV, Oct 07 2015

Scala

for (i <- 0 to 50) yield 17 * (i * i) // Alonso del Arte, Jun 29 2018

Formula

G.f.: 17*x*(1 + x)/(1 - x)^3. [corrected by Bruno Berselli, Jul 03 2014]

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

a(n) = 17*A000290(n). - Omar E. Pol, Jul 03 2014

a(n) = a(-n). - Muniru A Asiru, Jun 29 2018

From Elmo R. Oliveira, Dec 02 2024: (Start)

E.g.f.: 17*x*(1 + x)*exp(x).

a(n) = n*A008599(n) = A195047(2*n). (End)