A260857
Base-7 representation of a(n) is the concatenation of the base-7 representations of 1, 2, ..., n, n-1, ..., 1.
Original entry on oeis.org
0, 1, 64, 3249, 160000, 7845601, 384473664, 131870760799, 316621469105950, 760208147660763999, 1825259762561514314050, 4382448689911580334132199, 10522259304477772232578647150, 25263944590051134455098854865399, 60658730960712773989601560650105250
Offset: 0
a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = 64 = (7+1)^2 = 7^2 + 2*7 + 1 = 121_7 is the concatenation of (1, 2, 1).
a(8) = 316621469105950 = 123456101110654321_7 is the concatenation of (1, 2, 3, 4, 5, 6, 10, 11, 10, 6, 5, 4, 3, 2, 1), where the middle "10, 11, 10" are the base-7 representations of 7, 8, 7.
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Table[FromDigits[Flatten[Join[IntegerDigits[Range[n],7], IntegerDigits[ Range[ n-1,1,-1],7]]],7],{n,0,20}] (* Harvey P. Dale, Nov 02 2017 *)
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a(n,b=7)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))
A260858
Base-8 representation of a(n) is the concatenation of the base-8 representations of 1, 2, ..., n, n-1, ..., 1.
Original entry on oeis.org
0, 1, 81, 5329, 342225, 21911761, 1402427601, 89755965649, 45954960939217, 188231512819194065, 770996276517410920657, 3158000748616424634669265, 12935171066332946781853145297, 52982460687699754593548358342865, 217016158976818195107979529799293137
Offset: 0
a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = 81 = (8+1)^2 = 8^2 + 2*8 + 1 = 121_8, the concatenation of (1, 2, 1).
a(9) = 12345671011107654321_8, concatenation of (1, 2, 3, 4, 5, 6, 7, 10, 11, 10, 7, 6, 5, 4, 3, 2, 1), where the middle "10, 11, 10" are the base-8 representations of 8, 9, 8.
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a(n,b=8)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))
A260863
Base-13 representation of a(n) is the concatenation of the base-13 representations of 1, 2, ..., n, n-1, ..., 1.
Original entry on oeis.org
0, 1, 196, 33489, 5664400, 957345481, 161792190756, 27342890695849, 4620948663553600, 780940325907974961, 131978915101424183716, 22304436652439380447009, 3769449794266138309731600, 8281481197999449959084458465, 236527384496061684935031509169004
Offset: 0
a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = (13+1)^2 = 13^2 + 2*13 + 1 = 121_13, concatenation of (1, 2, 1).
a(14) = 123456789abc101110cba987654321_13 is the concatenation of (1, 2, 3, ..., 9, a, b, c, 10, 11, 10, c, ..., 1), where "c, 10, 11" are the base-13 representations of 12, 13, 14.
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a(n,b=13)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))
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