A118282 -id:A118282 - cp's OEIS frontend

A118283 Conjectured number of numbers that are not the sum of three generalized n-gonal numbers, or -1 if infinite.

0, -1, 0, 0, 4, -1, 26, 45, 94, -1, 196, -1, 370, -1, 641, 743, 999, -1, 1537, 1429, 2619

Offset: 3

T. D. Noe, Apr 21 2006

sign

See A118282 for the conjectured largest number that is not the sum of three generalized n-gonal numbers. For n=7, only four numbers are not representable: 10, 16, 76 and 307.

Cf. A118278-A118285.

A118286 Numbers n such that n == 0 (mod 4) or n == 2 (mod 12).

Original entry on oeis.org

2, 4, 8, 12, 14, 16, 20, 24, 26, 28, 32, 36, 38, 40, 44, 48, 50, 52, 56, 60, 62, 64, 68, 72, 74, 76, 80, 84, 86, 88, 92, 96, 98, 100, 104, 108, 110, 112, 116, 120, 122, 124, 128, 132, 134, 136, 140, 144, 146, 148, 152, 156, 158, 160, 164, 168, 170, 172, 176, 180, 182

Offset: 1

T. D. Noe, Apr 23 2006

Except for n=2, conjectured n such that A118278(n)=-1 and A118282(n)=-1; n such that there is an infinite set of numbers not representable as the sum of three n-gonal numbers or three generalized n-gonal numbers.

The difference between two consecutive terms follow the 4-period: (2, 4, 4, 2). - Bernard Schott, Feb 25 2019

Guenther Schrack, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Colin Barker)
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Cf. A047237, A118278, A118282.

Filtered([1..190],n->n mod 4=0 or n mod 12=2); # Muniru A Asiru, Feb 22 2019

[Round((3*n-1) + (Sqrt(-1))^n*(1+(-1)^n)/2): n in [1..70]]; // G. C. Greubel, Feb 21 2019

select(n->modp(n,4)=0 or modp(n,12)=2,[$1..190]); # Muniru A Asiru, Feb 22 2019

Mathematica
```
Union[4*Range[50], 2+12*Range[16]]
```

a(n) = (-2+(-I)^n+I^n+6*n)/2 \\ Colin Barker, Oct 19 2015

Vec(2*x*(1+2*x^2)/((1+x^2)*(1-x)^2) + O(x^70)) \\ Colin Barker, Oct 19 2015

for(n=1, 1e3, if(n%4 == 0 || n%12 == 2, print1(n", "))) \\ Altug Alkan, Oct 19 2015

[(3*n-1) + I^n*(1+(-1)^n)/2 for n in (1..70)] # G. C. Greubel, Feb 21 2019

G.f.: 2*x*(1+2*x^2) / ( (1+x^2)*(1-x)^2 ). - R. J. Mathar, Dec 02 2011
a(n) = 2*A047237(n+1) = 3*n - 1 + cos(n*Pi/2). - R. J. Mathar, Dec 02 2011
a(n) = (-2 + (-i)^n + i^n + 6*n)/2, where i = sqrt(-1). - Colin Barker, Oct 19 2015
a(n) = (6*n - 2 + (1 + (-1)^n)*(-1)^(n*(n-1)/2))/2. - Guenther Schrack, Feb 21 2019
E.g.f.: cos(x) + (3*x-1)*exp(x). - G. C. Greubel, Feb 21 2019

cp's OEIS Frontend

A118284 Conjectured largest number that is not the sum of three generalized (2n+1)-gonal numbers; bisection of A118282.

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A118283 Conjectured number of numbers that are not the sum of three generalized n-gonal numbers, or -1 if infinite.

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A118286 Numbers n such that n == 0 (mod 4) or n == 2 (mod 12).

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