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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.
1
0, 2, 7, 15, 25, 37, 52, 70, 90, 112, 137, 165, 195, 227, 262, 300, 340, 382, 427, 475, 525, 577, 632, 690, 750, 812, 877, 945, 1015, 1087, 1162, 1240, 1320, 1402, 1487, 1575, 1665, 1757, 1852, 1950, 2050, 2152, 2257
OFFSET
0,2
COMMENTS
a(-2)=2, a(-1)=0. 4 evens followed by 4 odds.
Last digit is only 0, 2, 5, 7.
The vertical spoke S-N of the pentagonal spiral for A004526.
37
37 25 25
36 24 15 15 26
36 24 14 7 8 16 26
35 23 14 7 2 3 8 16 27
35 23 13 6 2 0 0 3 9 17 27
34 22 13 6 1 1 4 9 17 28
34 22 12 5 5 4 10 18 28
33 21 12 11 11 10 18 29
33 21 20 20 19 19 29
32 32 31 31 30 30
Rank of multiples of 10: 0, 7, 8, 15, 16, ... = A047521. Compare to A154260 in the formula.
FORMULA
a(-1-n) = a(n).
a(2*n) + a(1+2*n) = 2, 22, 62, ... = A273366(n).
Second differences give the sequence of period 4: repeat [3, 3, 2, 2].
From Colin Barker, Feb 14 2020: (Start)
G.f.: x*(2 + x + 2*x^2) / ((1 - x)^3*(1 + x^2)).
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) for n>4.
(End)
Multiples of 10: 10*(0, 7, 9, 30, 34, ... = A154260).
4*a(n) = A087960(n) +5*n -1 +5*n^2. - R. J. Mathar, Feb 28 2020
MATHEMATICA
CoefficientList[Series[x (2 + x + 2 x^2)/((1 - x)^3*(1 + x^2)), {x, 0, 42}], x] (* Michael De Vlieger, Feb 14 2020 *)
PROG
(PARI) concat(0, Vec(x*(2 + x + 2*x^2) / ((1 - x)^3*(1 + x^2)) + O(x^40))) \\ Colin Barker, Feb 14 2020
CROSSREFS
Cf. A004526, A033429, A062786, A168668, A135706, A147874, 2*A147875 (all in the spiral).
Sequence in context: A350043 A375748 A167543 * A184976 A194140 A029888
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Feb 14 2020
STATUS
approved