A299267 Partial sums of A299266.

1, 6, 15, 37, 74, 131, 213, 330, 475, 653, 882, 1163, 1485, 1862, 2307, 2821, 3398, 4043, 4773, 5598, 6499, 7481, 8574, 9779, 11073, 12470, 13995, 15649, 17414, 19295, 21321, 23502, 25807, 28241, 30846, 33623, 36537, 39602, 42855, 46297, 49898, 53663, 57633, 61818, 66175, 70709, 75474, 80471, 85653, 91034, 96663

Offset: 0

Author

N. J. A. Sloane, Feb 07 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,3,-2,0,0,-2,3,-2,2,-1).

Crossrefs

Cf. A299266.

The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e: A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. See the Proserpio link in A299266 for overview.

Programs

Magma

I:=[15,37,74,131,213,330,475,653,882,1163,1485]; [1,6] cat [n le 11 select I[n] else 2*Self(n-1) -2*Self(n-2) +3*Self(n-3)-2*Self(n-4)-2*Self(n-7) +3*Self(n-8) -2*Self(n-9)+2*Self(n-10)-Self(n-11): n in [1..30]]; // G. C. Greubel, Feb 20 2018

Mathematica

CoefficientList[Series[(1 +4*x +5*x^2 +16*x^3 +14*x^4 +24*x^5 +18*x^6 +20*x^7 +5*x^8 + x^10 -4*x^11 +4*x^12)/((1 -x)^4*(1 +x)*(1 +x^2)^2*(1 +x +x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 20 2018 *)
LinearRecurrence[{2,-2,3,-2,0,0,-2,3,-2,2,-1},{1,6,15,37,74,131,213,330,475,653,882,1163,1485},60] (* Harvey P. Dale, Sep 03 2018 *)

PARI

Vec((1 + 4*x + 5*x^2 + 16*x^3 + 14*x^4 + 24*x^5 + 18*x^6 + 20*x^7 + 5*x^8 + x^10 - 4*x^11 + 4*x^12) / ((1 - x)^4*(1 + x)*(1 + x^2)^2*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, Feb 15 2018

Formula

From Colin Barker, Feb 15 2018: (Start)

G.f.: (1 +4*x +5*x^2 +16*x^3 +14*x^4 +24*x^5 +18*x^6 +20*x^7 +5*x^8 + x^10 -4*x^11 +4*x^12)/((1 -x)^4*(1 +x)*(1 +x^2)^2*(1 +x +x^2)).

a(n) = 2*a(n-1) - 2*a(n-2) + 3*a(n-3) - 2*a(n-4) - 2*a(n-7) + 3*a(n-8) - 2*a(n-9) + 2*a(n-10) - a(n-11) for n>12.

(End)