A075666
Sum of next n 5th powers.
Original entry on oeis.org
1, 275, 11925, 208624, 2078375, 14118201, 72758875, 304553600, 1084203549, 3390961375, 9540835601, 24582546000, 58801331875, 131987718149, 280410672375, 567799960576, 1102105900025, 2060382328875, 3724847929549, 6534040766000, 11154010982751, 18575718271825
Offset: 1
a(1) = 1^5 = 1; a(2) = 2^5 + 3^5 = 275; a(3) = 4^5 + 5^5 + 6^5 = 11925; a(4) = 7^5 + 8^5 + 9^5 + 10^5 = 208624.
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
-
i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=5; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
nn=30;With[{p5=Range[((nn+1)(nn+2))/2]^5},Join[{1},Table[Total[Take[p5,{(n(n+1))/2+1,((n+1)(n+2))/2}]],{n,nn}]]] (* Harvey P. Dale, Mar 09 2014 *)
Module[{nn=25,p5},p5=Range[(nn(nn+1))/2]^5;Total/@TakeList[p5,Range[nn]]] (* Harvey P. Dale, Oct 13 2023 *)
A075667
Sum of next n 6th powers.
Original entry on oeis.org
1, 793, 66377, 1911234, 28504515, 271739011, 1874885963, 10136389172, 45311985069, 173957200405, 589679082421, 1802148522758, 5045944649967, 13108508706879, 31915866810295, 73427944186856, 160710828298553, 336507487921137, 677266380588289, 1315464522556810
Offset: 1
a(1) = 1^6 = 1; a(2) = 2^6 + 3^6 = 793; a(3) = 4^6 + 5^6 + 6^6 = 66377; a(4) = 7^6 + 8^6 + 9^6 + 10^6 = 1911234.
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
-
i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=6; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
With[{nn=20},Total/@TakeList[Range[(nn(nn+1))/2]^6,Range[nn]]] (* or *) LinearRecurrence[{14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1},{1,793,66377,1911234,28504515,271739011,1874885963,10136389172,45311985069,173957200405,589679082421,1802148522758,5045944649967,13108508706879},20] (* Harvey P. Dale, Mar 29 2022 *)
A075668
Sum of next n 7th powers.
Original entry on oeis.org
1, 2315, 374445, 17703664, 394340375, 5265954441, 48574262275, 338837482880, 1900477947429, 8950536157375, 36536761179281, 132397570996560, 433806511149115, 1303971065324669, 3637715990646375, 9507513902672896, 23461050872397545, 55013865421504275
Offset: 1
a(1) = 1^7 = 1; a(2) = 2^7 + 3^7 = 2315; a(3) = 4^7 + 5^7 + 6^7 = 374445; a(4) = 7^7 + 8^7 + 9^7 + 10^7 = 17703664.
- Kelvin Voskuijl, Table of n, a(n) for n = 1..10000
- Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
-
i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=7; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
A075669
Sum of next n 8th powers.
Original entry on oeis.org
1, 6817, 2135777, 165588738, 5498750979, 102697107715, 1264908663011, 11373936899396, 79985007371877, 461856872635333, 2269365182729029, 9747136491367430, 37362375267437415, 129917413702762791, 415196000174767687, 1232554282743058568, 3428668198703973449
Offset: 1
a(1) = 1^8 = 1; a(2) = 2^8 + 3^8 = 6817; a(3) = 4^8 + 5^8 + 6^8 = 2135777; a(4) = 7^8 + 8^8 + 9^8 + 10^8 = 165588738.
- Kelvin Voskuijl, Table of n, a(n) for n = 1..10000
- Index entries for linear recurrences with constant coefficients, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).
-
i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=8; Table[Sum[i^s, {i, i1, i2}], {n, 20}]