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 A298397 Pentagonal numbers divisible by 4. 1
 0, 12, 92, 176, 376, 532, 852, 1080, 1520, 1820, 2380, 2752, 3432, 3876, 4676, 5192, 6112, 6700, 7740, 8400, 9560, 10292, 11572, 12376, 13776, 14652, 16172, 17120, 18760, 19780, 21540, 22632, 24512, 25676, 27676, 28912, 31032, 32340, 34580, 35960, 38320, 39772, 42252 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If b(n) is the n-th octagonal number multiple of 32 then a(n) = b(n)/8. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA O.g.f.: 4*x^2*(3 + 20*x + 15*x^2 + 10*x^3)/((1 + x)^2*(1 - x)^3). E.g.f.: (33 - 32*x + 24*x^2)*exp(x) + (7 + 6*x)*exp(-x) - 40. a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). a(n) = 8*n*(3*n - 7) - (6*n - 7)*(-1)^n + 33. From Colin Barker, Jan 20 2018: (Start) a(n) = 24*n^2 - 62*n + 40 for n even. a(n) = 24*n^2 - 50*n + 26 for n odd. (End) EXAMPLE A000326(8) = 92 is in the sequence because 92 = 4*23. MAPLE P:=proc(n) local x; x:=n*(3*n-1)/2; if x mod 4=0 then x; fi; end: seq(P(i), i=0..2*10^2); # Paolo P. Lava, Jan 19 2018 MATHEMATICA Table[8 n (3 n - 7) - (6 n - 7) (-1)^n + 33, {n, 1, 50}] (* Second program (using definition): *) Select[Table[k*(3*k - 1)/2, {k, 0, 200}], Divisible[#, 4]&] (* Jean-François Alcover, Jan 19 2018 *) PROG (PARI) vector(50, n, nn; 8*n*(3*n-7)-(6*n-7)*(-1)^n+33) (Sage) [8*n*(3*n-7)-(6*n-7)*(-1)^n+33 for n in (1..50)] (Maxima) makelist(8*n*(3*n-7)-(6*n-7)*(-1)^n+33, n, 1, 50); (Magma) [8*n*(3*n-7)-(6*n-7)*(-1)^n+33: n in [1..50]]; (GAP) List([1..50], n -> 8*n*(3*n-7)-(6*n-7)*(-1)^n+33); (PARI) concat(0, Vec(4*x^2*(3 + 20*x + 15*x^2 + 10*x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40))) \\ Colin Barker, Jan 20 2018 CROSSREFS Cf. A000326, A000567. Subsequence of A047217, A047388. Cf. pentagonal numbers divisible by k: A014633 (k=2), A268351 (k=3), this sequence (k=4), A117793 (k=5). Sequence in context: A160869 A026074 A339715 * A246585 A120990 A220330 Adjacent sequences: A298394 A298395 A298396 * A298398 A298399 A298400 KEYWORD nonn,easy AUTHOR Bruno Berselli, Jan 18 2018 STATUS approved

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Last modified December 2 16:47 EST 2023. Contains 367525 sequences. (Running on oeis4.)