A074622 -id:A074622 - cp's OEIS frontend

A245807 a(n) = 7^n + 10^n.

2, 17, 149, 1343, 12401, 116807, 1117649, 10823543, 105764801, 1040353607, 10282475249, 101977326743, 1013841287201, 10096889010407, 100678223072849, 1004747561509943, 10033232930569601, 100232630513987207, 1001628413597910449, 10011398895185373143

Offset: 0

Vincenzo Librandi, Aug 04 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (17,-70).

Cf. 7^n+k^n: A034491 (k=1), A074602 (k=2), A074608 (k=3), A074613 (k=4), A074616 (k=5), A074619 (k=6), A109808 (k=7), A074622 (k=8), A074623 (k=9), this sequence (k=10).

Magma
```
[7^n+10^n: n in [0..25]];
```

I:=[2,17]; [n le 2 select I[n] else 17*Self(n-1)-70*Self(n-2): n in [1..25]];

Table[(7^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 17 x)/((1 - 7 x) (1 - 10 x)), {x, 0, 40}], x]

G.f.: (2-17*x)/((1-7*x)*(1-10*x)).
E.g.f.: e^(7*x) + e^(10*x).
a(n) = 17*a(n-1)-70*a(n-2).
a(n) = A000420(n) + A011557(n).

A210694 T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.

Original entry on oeis.org

5, 13, 9, 25, 35, 17, 41, 91, 97, 33, 61, 189, 337, 275, 65, 85, 341, 881, 1267, 793, 129, 113, 559, 1921, 4149, 4825, 2315, 257, 145, 855, 3697, 10901, 19721, 18571, 6817, 513, 181, 1241, 6497, 24583, 62281, 94509, 72097, 20195, 1025, 221, 1729, 10657, 49575

Offset: 1

R. H. Hardin, with R. J. Mathar in the Sequence Fans Mailing List, Mar 30 2012

Table starts
...5....13.....25......41.......61.......85.......113.......145........181
...9....35.....91.....189......341......559.......855......1241.......1729
..17....97....337.....881.....1921.....3697......6497.....10657......16561
..33...275...1267....4149....10901....24583.....49575.....91817.....159049
..65...793...4825...19721....62281...164305....379793....793585....1531441
.129..2315..18571...94509...358061..1103479...2920695...6880121...14782969
.257..6817..72097..456161..2070241..7444417..22542017..59823937..143046721
.513.20195.281827.2215269.12030821.50431303.174571335.521638217.1387420489
Solutions are determined by the diagonal, extended with x(i,j) = (x(i,i)+x(j,j))/2 * (-1)^(i-j)

			Some solutions for n=3 k=4
.-2..1.-3..0....0.-1..0..1....4..0..1.-1....2.-1.-1.-2....3.-2..1..0
..1..0..2..1...-1..2.-1..0....0.-4..3.-3...-1..0..2..1...-2..1..0.-1
.-3..2.-4..1....0.-1..0..1....1..3.-2..2...-1..2.-4..1....1..0.-1..2
..0..1..1..2....1..0..1.-2...-1.-3..2.-2...-2..1..1..2....0.-1..2.-3

R. H. Hardin, Table of n, a(n) for n = 1..10000

cf. A179927
Column 1 is A000051(n+1)
Column 2 is A007689(n+1)
Column 3 is A074605(n+1)
Column 4 is A074611(n+1)
Column 5 is A074615(n+1)
Column 6 is A074619(n+1)
Column 7 is A074622(n+1)
Column 8 is A074624(n+1)
Row 1 is A001844
Row 2 is A005898
Row 3 is A008514
Row 4 is A008515
Row 5 is A008516
Row 6 is A036085
Row 7 is A036086
Row 8 is A036087

T(n,k)=k^(n+1)+(k+1)^(n+1)

A221904 a(n) = 9^n + 10^n.

Original entry on oeis.org

2, 19, 181, 1729, 16561, 159049, 1531441, 14782969, 143046721, 1387420489, 13486784401, 131381059609, 1282429536481, 12541865828329, 122876792454961, 1205891132094649, 11853020188851841

Offset: 0

Vincenzo Librandi, Feb 06 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (19,-90).

Cf. A007689, A074611, A074615, A074619, A074622, A074624, A155872.

Magma
```
[9^n + 10^n: n in [0..30]];
```

CoefficientList[Series[1/(1-9*x) + 1/(1-10*x), {x, 0, 30}], x]
LinearRecurrence[{19,-90},{2,19},30] (* Harvey P. Dale, Nov 10 2017 *)

G.f.: 1/(1 - 9*x) + 1/(1 - 10*x).
E.g.f.: exp(9*x) + exp(10*x).
a(n) = 19*a(n-1) - 90*a(n-2), a(1)=2, a(2)=19.

cp's OEIS Frontend

A245807 a(n) = 7^n + 10^n.

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A210694 T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.

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Formula

A221904 a(n) = 9^n + 10^n.

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Magma

Mathematica

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