cp's OEIS Frontend

A332495 a(n-2) = a(n-6) + 5*(1+2*n) with a(0)=0, a(1)=2, a(2)=7, a(3)=15 for n>=4.

%I A332495 #17 Mar 18 2020 13:01:37
%S A332495 0,2,7,15,25,37,52,70,90,112,137,165,195,227,262,300,340,382,427,475,
%T A332495 525,577,632,690,750,812,877,945,1015,1087,1162,1240,1320,1402,1487,
%U A332495 1575,1665,1757,1852,1950,2050,2152,2257
%N A332495 a(n-2) = a(n-6) + 5*(1+2*n) with a(0)=0, a(1)=2, a(2)=7, a(3)=15 for n>=4.
%C A332495 a(-2)=2, a(-1)=0. 4 evens followed by 4 odds.
%C A332495 Last digit is only 0, 2, 5, 7.
%C A332495 The vertical spoke S-N of the pentagonal spiral for A004526.
%C A332495                           37
%C A332495                       37  25  25
%C A332495                   36  24  15  15  26
%C A332495               36  24  14   7   8  16  26
%C A332495           35  23  14   7   2   3   8  16  27
%C A332495       35  23  13   6   2   0   0   3   9  17  27
%C A332495         34  22  13   6   1   1   4   9  17  28
%C A332495           34  22  12   5   5   4  10  18  28
%C A332495             33  21  12  11  11  10  18  29
%C A332495               33  21  20  20  19  19  29
%C A332495                 32  32  31  31  30  30
%C A332495 Rank of multiples of 10: 0, 7, 8, 15, 16, ... = A047521. Compare to A154260 in the formula.
%H A332495 Colin Barker, <a href="/A332495/b332495.txt">Table of n, a(n) for n = 0..1000</a>
%H A332495 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,4,-3,1).
%F A332495 a(-1-n) = a(n).
%F A332495 a(2*n) + a(1+2*n) = 2, 22, 62, ... = A273366(n).
%F A332495 Second differences give the sequence of period 4: repeat [3, 3, 2, 2].
%F A332495 From _Colin Barker_, Feb 14 2020: (Start)
%F A332495 G.f.: x*(2 + x + 2*x^2) / ((1 - x)^3*(1 + x^2)).
%F A332495 a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) for n>4.
%F A332495 (End)
%F A332495 Multiples of 10: 10*(0, 7, 9, 30, 34, ... = A154260).
%F A332495 4*a(n) = A087960(n) +5*n -1 +5*n^2. - _R. J. Mathar_, Feb 28 2020
%t A332495 CoefficientList[Series[x (2 + x + 2 x^2)/((1 - x)^3*(1 + x^2)), {x, 0, 42}], x] (* _Michael De Vlieger_, Feb 14 2020 *)
%o A332495 (PARI) concat(0, Vec(x*(2 + x + 2*x^2) / ((1 - x)^3*(1 + x^2)) + O(x^40))) \\ _Colin Barker_, Feb 14 2020
%Y A332495 Cf. A004526, A033429, A062786, A168668, A135706, A147874, 2*A147875 (all in the spiral).
%Y A332495 Cf. A005408, A047521, A154260
%K A332495 nonn,easy
%O A332495 0,2
%A A332495 _Paul Curtz_, Feb 14 2020